Why not adjusting the number of friends

I am trying to simulate the unexpected social consequences due to a change in policy. This is “demo 3” of Matt’s proposed paper.

My initial focus was on changing the number of friends with some adaptive rule and then see if policies had any effect. The results however were unimpressive. In most cases the correlation between number of friends and profitability is weak enough that an adaptive agent trying to adjust its network degree proceeds by almost complete random walk. It’s just hard to hill-climb a very noisy surface. Policy would have some effect (in particular if quotas were set very low) but not strong enough to generate large changes in social networks.

My suspicion is that we are replicating the results in Little and MacDonald (2007) where it is the structure of the social network rather than the raw number of links that drive overall fishery results. That is probably the case here too but it’s a deep rabbit hole I have no time to jump into at the present time.

Adapting Adaptors

Take instead the more discrete, and familiar, problem of agents choosing to be either explorers (stochasts) or imitators (cartesian). Ren’s implementation of these two strategies is cool (explorers act completely at random, imitators copy the global best) but here i implement them slightly less extreme version of the two.

  1. Explorers use the \(\epsilon\)-greedy bandit algorithm described in section 2.2 of the algorithms paper
  2. Imitators use the gravitational search algorithm described in section 3.2

Every 2 months, each agent has a 20% chance of deciding whether to switch strategy or not (adding inertia is always smart in evolutionary game theory with global replicators like here). It does so by soft-max so that, knowing the average profitability of strategy \(i\) as \(\pi_i\), the agent picks strategy \(i\) with probability: \[ P(i) = \frac{e^{\pi_i}}{\sum_{j}^N e^{\pi_j}} \] Where \(N\) is the number of strategies available (2 in this case). I like this because we can use it to pick among many strategies when the time comes.

Now we have a simple adaptive rule for agents to switch strategy back and forth. Let’s see what happens when we adjust policies. We start with four scenarios:

I try the following policies: - Anarchy: no rules - High-ITQ: quotas for 8000 units of fish per fisher - ITQ: quotas for 4000 units of fish per fisher - Low-ITQ: quotas for 2000 units of fish per fisher - TAC: global quota for 4000 units of fish per fisher

I run each scenario-policy pair 100 times for 15 simulated years, then boxplot the number of imitators at the end of the simulation.

Mechanically we can run an anova to make sure that policies do indeed affect the average, which they strongly do.

scenario p.value
standard 5.861017e-07
chaser 0.000000e+00
fixed dynamic 0.000000e+00
no regrowth big 1.238955e-11

Graphically however it looks like that the chaser and the fixed dynamic scenarios have particularly large changes and so worth studying in depth.

Fixed Dynamic

The key feature of the fixed dynamic adaptation is that when quotas are introduced (both ITQ and TACs) you have a population that reacts by basically becoming 100% imitative. This is due to two factors. First, when quotas are small most of the fishing will happen within the first few months (after which you hit the quota and the fishery closes). Second, during the first few months the biomass is concentrated around port and migrates towards away the end of the year. Exploration is beneficial (personally and to society) only towards the end of the year, not the beginning of it. So when quotas are imposed agents learn that exploration is futile and simply copy one another at staying near port.

To see what is happening, here’s a plot showing the time series of imitators over the course of each run. Each line represents the # of imitators at that day for that run. Strictly speaking this should be a “step-wise” graph (since the adaption occurs only every 2 months) but it’s a lot clearer when simplified to a straight line.

What is happening is that invariably at the beginning of the year people shift towards imitative strategies (imitating being near port) but towards the end of the year they move towards more exploratory strategies since the fish spreads out far from port.

What happens when we impose a TAC? Agents fish the quota out during the first few months of simulation and then the fishery close. Since the fishery is closed when the fish migrates out there is never any benefit in being an explorer. This becomes apparent and every year the number of imitators increase by a little bit:

Chaser

While they look quite small, the changes in the the chaser scenario are very important. The fact is that schooling is a scenario where imitation (as gravitational-search) performs much better than exploration (\(\epsilon\)-greedy) in almost all cases. In fact GSA tends to beat all the other algorithms, as shown in figure 4.10 of the algorithms paper. Moreover that figure also shows that \(\epsilon\)-greedy produces negative profits on average in this scenario.

However it is interesting to look at the time series of strategiess. What happens is that while there is clearly a switch towards GSA, sometimes the number of imitators drop. This happens whenever there is a large group of imitators that “lose track” of the school. At which point they make consistently negative profits and some switch back to exploring. This only lasts for a bit however because as soon as somebody spots the fish school all the imitators catch it and at that point imitating becomes better again. This results in all runs ending up with 100% imitators.

What happens when a TAC is introduced? Well, most years actually not much happens because it turns out that the fish is far enough from port that agents barely even hit the quota. Those years the number of imitators grow as usual. However in the years where the fish is near port the quota is consumed quite quickly and the fishery closes for long periods of time.

The fish school keeps moving while the fishery is closed however and when the fishing season opens again nobody has a any clue where the fish is. Imitators go back to the old spot and find nothing, losing money.
Eventually people switch to explorators until enough fishers hit the school again and the remaining imitators chase it. This in turn make people move to imitation until the next time the fishery is closed at which point the cycle restarts.

Efficiency

It’s actually interesting to notice that if we compare the various scenarios by catches per unit of effort, then the chaser scenario has lower efficiency when a TAC is introduced (to account for fishers losing track of where the fish is) while the fixed-dynamic scenario has much higher CPUE due to restricting fishing to only periods where the fish is extremely abundant and next to port.